Analogous to the boundary-fitted case, shape functions are introduced on the active mesh \(\mathcal {T}_h\)  and an approximate solution \(u_h\)  is formed as a linear combination of the restriction of the shape functions to \(\Omega \) . The space spanned by these functions is referred to as \(V_h\) . In contrast to the boundary-fitted finite element formulation, in the unfitted setting it is generally not feasible to create a finite dimensional subspace of \(V_{h,0} \subset H^1_0(\Omega )\) , which is needed to strongly impose Dirichlet conditions. Instead, Dirichlet conditions are generally imposed weakly. The most common approach for weakly enforcing Dirichlet boundary conditions is via Nitsche's method [1]}, which gives rise to the immersed finite element formulation
\(\text{(Immersed FE)}{\left\lbrace \begin{array}{ll}\text{find } u_h \in V_{h} \text{ such that:}\\a_h(u_h,v_h) = l_h(v_h) \qquad \forall v_h \in V_{h}\end{array}\right.}\) 
